Functions, inverse & composite functions

The function f is defined as

State the value of x that cannot be included in any domain of the function f

Express the inverse function f^–1 in the form f^–1(x) =...

f^–1(x) =_........

The functions f and g are such that

State which value of x cannot be included in any domain of g

Find fg(4)

The function h is such that

Express the inverse function h⁻¹ in the form h¹:x ...

The functions g and h are such that

h(x) = x² + 4 x 0

What value of x must be excluded from any domain of g?

Solve gh(x) = 1

The function f is such that

Find f^–1(x)

The function g is such that

Express g(x) in the form a(x – b)² + c

The function f is defined as

Find f(10)

Express the inverse function f⁻¹ in the form f⁻¹:x …

f⁻¹:x _........

The function g is defined as

Express the inverse function g⁻¹ in the form g⁻¹:x …

g⁻¹:x _........

State the domain of g⁻¹

The functions f and g are defined as

f(x) = x² + 6 g(x) = x – 10

Find fg(3)

Solve the equation fg(x) = f(x) Show clear algebraic working.

The function h is defined as

State the value of x that cannot be included in the domain of h

Express the inverse function h^–1 in the form h^–1(x) =...

h^–1(x) =_........

The functions f and g are defined as

f:x 5x – 7

Write down the value of x that must be excluded from any domain of g

Find gf(2.6)

Solve fg(x) = 2

Express the inverse function g^–1 in the form g^–1:x ...

g^–1:x _........

Find f (1)

State the range of the function f.

The function g is such that g(x) = x ≠−3

Work out fg(2)

Use the graph to find an estimate for the gradient of the curve at P.

Hence find an equation of the tangent to the curve at P. Give your answer in the form y=mx+c

The equation f (x) =k has exactly two different solutions for −4≤ x ≤12

Use the graph to find the two possible values of k.

The functions f and g are defined as

State which value of x must be excluded from any domain of the function f.

Find fg(x). Simplify your answer.

fg(x) =_........

Express the inverse function f in the form f (x) = …

f (x) =_........

Part of the curve with equation y = h(x) is shown on the grid.

Find an estimate for the gradient of the curve at the point where x Show your working clearly.

The function f is such that f (x) = 3 x – 2

Find f (5)

The function g is such that g(x) = 2x² – 20x + 9 where x 5

Express the inverse function g^–1 in the form g^–1(x) =...

g^–1(x) =_........

The function f is such that

Find f (–7)

Express the inverse function f^–1 in the form f^–1(x) =...

The function g is such that

Find fg (3)

Which values of x cannot be included in any domain of g?